Abstract
The theory of optimal experimental designs is concerned with the construction of designs that are optimum with respect to some statistical criteria. Some of these criteria include the alphabetic optimality criteria such as; D-, A-, E-, T-, G- and C- criterion. Compound optimality criteria are those that combine two or more alphabetic optimality criteria. Design that require optimality criteria have specific desired properties that do very well in one design and at the same time perform poorly in another design. Thus, a compound optimality criterion gives a balance to the desirability of any two or more alphabetic optimality criteria. The present paper aims to introduce CD- and DT- criteria which are compound optimality criteria for second order rotatable designs constructed using Balanced Incomplete Block Designs (BIBDs) in four dimensions.
Highlights
Design experts have come to a realization that a design can perform very well in terms of a particular statistical characteristic and still perform poorly in terms of a rival characteristic
This paper combines two alphabetic optimality criteria Dand T- by using the concept that was introduced by Atkinson [10], where DT optimality criterion is a combination of Doptimality criterion for parameter estimation with the Toptimality criterion for discriminating between models
The study concludes by combining D- and trace criterion (T-)optimality to get DT-(compound optimality)
Summary
Design experts have come to a realization that a design can perform very well in terms of a particular statistical characteristic and still perform poorly in terms of a rival characteristic. Box and Wilson [1] suggest using a second-degree polynomial model to do this They acknowledge that this model is only an approximation, but they use it because such a model is easy to estimate and apply, even when little is known about the process. Statistical approaches such as RSM can be employed to maximize the production of a special substance by optimization of operational factors. According to Box and Draper [3], RSM is either used to explore response surfaces or to estimate the parameters of a model. I =1 i =1 i∠j where is the intercept is the linear coefficient for the ith factor is the quadratic coefficient for the ithfactors is the cross product coefficient for the ith and jth factors is the level of the ith factor is the level of the ith and jth factor
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